1. Field of the Invention
The present invention relates to a topography simulation method. More particularly, the present invention concerns a simulation method which enables estimation of the three-dimensional shape of a region of a workpiece to be removed in the manufacture of a semiconductor device.
2. Description of the Related Art
Simulation of, for example, an etched profile in etching is performed conventionally on the basis of the string model using a computer. FIG. 1 is a cross-sectional view of the shape of the surface to be etched which is obtained by simulation by means of the string model. In FIG. 1, reference numerals 1 and 2 denote a semiconductor substrate, and a resist, respectively. The resist 2 prevents the semiconductor substrate 1 from being etched. The semiconductor substrate 1 is selectively etched with this resist 2 as a mask. The shape of the surface to be etched is represented by a plurality of nodes 21 and segments 22 that connect the adjacent nodes 21. The etching is performed by advancing the individual nodes 21 in the direction indicated by arrows 23. Movement of the individual nodes 21 is determined at intervals of .DELTA.t seconds, which is a short period of time. Each time they are determined, the corresponding two nodes 21 are connected with each other by the segment 22. At that time, the nodes 21 and the segments 22, must be controlled so that the length of the individual segments 22 does not become excessively long or short or so that the two segments 22 do not intersect.
FIG. 2 shows conceptually a control of the string which is applied to isotropic etching. Let the coordinates of three points 24, 25 and 26 on the surface to be etched at time ti be (i, j-1), (i, j) and (i, j+1), respectively. The point 25 moves to and is located at point 27 having the coordinates (i+1, j) .DELTA.t seconds after time ti, which is time ti+1 . Assuming that etching propagates at this time at an etching velocity of (i, v), the relation between the points 25 and 27 is expressed by the following equation. EQU (i+1, j)=(i, j)+(i, v).times..DELTA.t.
Where (i, j.fwdarw.j-1 ) is a vector 29 which is directed from the point 25 to the point 24 at time ti, (i, j.fwdarw.j+1) is a vector 30 which is directed from the point 25 to the point 26, and .vertline.i, j.fwdarw.j-1.vertline. and .vertline.i, j-j+1.vertline. are respectively the magnitudes of the vectors 29 and 30, the direction of the etching velocity 28 is determined by: ##EQU1##
The string model is thus controlled to enable simulation of, for example, a two-dimensional topography.
When this string model is applied to the simulation of a three-dimensional topography, the three-dimensional shape is represented by a plurality of small triangles, and movements of the individual triangles are determined at the intervals of .DELTA.t.
However, control of the dimension and the intersection of the individual triangles requires extremely complicated programming of a computer, long operation time and a large memory capacity, and this makes simulation of a three-dimensional topography using the string model substantially impossible.